Nuprl Lemma : fun-ss_wf
∀[ss:SeparationSpace]. ∀[A:Type]. (A ⟶ ss ∈ SeparationSpace)
Proof
Definitions occuring in Statement :
fun-ss: A ⟶ ss,
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
ss-point: Point,
ss-sep: x # y,
or: P ∨ Q,
guard: {T},
btrue: tt,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
record-select: r.x,
record+: record+,
separation-space: SeparationSpace,
subtype_rel: A ⊆r B,
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
exists: ∃x:A. B[x],
fun-sep: fun-sep(ss;A;f;g),
false: False,
implies: P ⇒ Q,
not: ¬A,
all: ∀x:A. B[x],
fun-ss: A ⟶ ss,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
separation-space_wf,
equal_wf,
or_wf,
ss-sep_wf,
subtype_rel_self,
not_wf,
all_wf,
ss-sep-irrefl,
fun-sep_wf,
ss-point_wf,
mk-ss_wf
Rules used in proof :
isect_memberEquality,
axiomEquality,
dependent_functionElimination,
inrEquality,
inlEquality,
unionElimination,
rename,
setElimination,
because_Cache,
equalitySymmetry,
equalityTransitivity,
setEquality,
universeEquality,
instantiate,
tokenEquality,
dependentIntersectionEqElimination,
dependentIntersectionElimination,
dependent_pairEquality,
productEquality,
spreadEquality,
voidElimination,
independent_functionElimination,
productElimination,
lambdaFormation,
applyEquality,
functionExtensionality,
lambdaEquality,
dependent_set_memberEquality,
hypothesis,
hypothesisEquality,
cumulativity,
functionEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[ss:SeparationSpace]. \mforall{}[A:Type]. (A {}\mrightarrow{} ss \mmember{} SeparationSpace)
Date html generated:
2016_11_08-AM-09_11_56
Last ObjectModification:
2016_11_02-AM-11_09_02
Theory : inner!product!spaces
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